Subgroups — D₆₇×C₃⋊D₃₃ #40997708

Order 26532.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×C₃⋊D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₃×D₆₇	—	3	4	no	maximal
5	C₃²×C₁₁×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₂₁₁	—	3	4	no	—
7	D₃₃×C₆₇	—	3	4	no	—
8	C₃×C₁₁×D₆₇	D₃	1	4	yes	complemented
9	D₁₁×D₆₇	—	9	1	no	Hall
10	C₃⋊D₃×D₆₇	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₆₇	C₂×D₃	1	4	yes	complemented
12	D₇₃₇	—	9	1	no	—
13	C₁₁×D₆₇	C₃⋊D₃	1	1	yes	characteristic, complemented
14	D₁₁×C₆₇	—	9	1	no	—
15	C₃⋊D₂₀₁	—	11	1	no	—
16	C₃⋊D₃×C₆₇	—	11	1	no	—
17	C₃²×D₆₇	D₁₁	1	1	yes	characteristic, complemented
18	D₃×D₆₇	—	33	4	no	—
19	C₁₁×C₆₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	D₂₀₁	—	33	4	no	—
22	C₃×D₆₇	D₃₃	1	4	yes	complemented
23	D₃×C₆₇	—	33	4	no	—
24	C₂×C₃⋊D₃₃	—	67	1	no	maximal, Hall
25	C₂×D₆₇	—	99	1	no	Hall
26	C₃×C₆₇	C₂×D₃₃	1	4	yes	complemented
27	C₂×C₃²×C₁₁	—	67	1	no	—
28	C₃⋊D₃₃	—	67	1	no	—
29	C₃⋊D₃₃	D₆₇	1	1	yes	characteristic, direct product factor
30	C₂×C₆₇	—	99	1	no	—
31	D₆₇	—	99	1	no	—
32	D₆₇	C₃⋊D₃₃	1	1	yes	characteristic, direct product factor
33	C₂×D₃₃	—	201	4	no	—
34	C₃²×C₁₁	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
35	C₆₇	C₂×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₁	—	67	4	no	—
37	D₃₃	—	3	4	no	—
38	D₃₃	—	201	4	no	—
39	C₂×D₁₁	—	603	1	no	Hall
40	C₂×C₃⋊D₃	—	737	1	no	Hall
41	C₃×C₁₁	D₃×D₆₇	1	4	yes	complemented
42	C₂×C₁₁	—	67	1	no	—
43	D₁₁	—	9	1	no	—
44	D₁₁	—	603	1	no	—
45	C₂×C₃²	—	67	1	no	—
46	C₃⋊D₃	—	11	1	no	—
47	C₃⋊D₃	—	737	1	no	—
48	C₂×D₃	—	2211	4	no	—
49	C₁₁	C₃⋊D₃×D₆₇	1	1	yes	characteristic, complemented, Sylow
50	C₃²	D₁₁×D₆₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	67	4	no	—
52	D₃	—	33	4	no	—
53	D₃	—	2211	4	no	—
54	C₂²	—	6633	1	no	Sylow
55	C₃	D₃₃×D₆₇	1	4	yes	complemented
56	C₂	—	67	1	no	—
57	C₂	—	99	1	no	—
58	C₂	—	6633	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁×C₆₇	C₂²
LCS	G ▷ C₃²×C₁₁×C₆₇
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₁₁×D₆₇	C₂	semidirect
2. C₆₇×C₃⋊D₃₃	C₂	semidirect
3. C₃⋊D₂₂₁₁	C₂	semidirect
5. C₃²×C₁₁×C₆₇	C₂²	semidirect
8. C₃×C₁₁×D₆₇	D₃	semidirect
11. C₃×C₁₁×C₆₇	C₂×D₃	semidirect
13. C₁₁×D₆₇	C₃⋊D₃	semidirect
17. C₃²×D₆₇	D₁₁	semidirect
19. C₁₁×C₆₇	C₂×C₃⋊D₃	semidirect
20. C₃²×C₆₇	C₂×D₁₁	semidirect
22. C₃×D₆₇	D₃₃	semidirect
26. C₃×C₆₇	C₂×D₃₃	semidirect
29. C₃⋊D₃₃	D₆₇	direct (N × H)
32. D₆₇	C₃⋊D₃₃	direct (N × H)
34. C₃²×C₁₁	C₂×D₆₇	semidirect
35. C₆₇	C₂×C₃⋊D₃₃	semidirect
41. C₃×C₁₁	D₃×D₆₇	semidirect
49. C₁₁	C₃⋊D₃×D₆₇	semidirect
50. C₃²	D₁₁×D₆₇	semidirect
55. C₃	D₃₃×D₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₁₁×D₆₇	2
C₆₇×C₃⋊D₃₃	2
C₃⋊D₂₂₁₁	2
D₃₃×D₆₇	3
C₃⋊D₃×D₆₇	11
C₂×C₃⋊D₃₃	67

Subgroups — D67×C3⋊D33 #40997708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₇×C₃⋊D₃₃ #40997708